On the damping intensity of the odd Fourier impulse loading the boundary of the periodic composite

Main Article Content

D. Kula

Keywords : heat transfer, Fourier series, tolerance averaging, micro-macro hypothesis, surface localization, effective conductivity

Investigated in the paper boundary effect behaviour for a single odd amplitude which loads rectangular boundary of the two-phased periodic composite layer confirms the common view through the prism of the expected strong suppression of the boundary impulses of the physical field near the boundary of the region occupied by the composite. There is no presence of a composite reaction to the boundary loadings mentioned here different than the exponential damping effect. However, the presence in the general equation describing the boundary effect equations the component 2?ssurf pqz?q with the first space derivative responsible for suppression of the solution along the axis Oz should cause not only exponential type of boundary temperature fluctuation damping. This component disappears in principle for the boundary effect analysed for a single impulse.

Article Details

How to Cite
Kula, D. (2019). On the damping intensity of the odd Fourier impulse loading the boundary of the periodic composite. Scientific Review Engineering and Environmental Studies (SREES), 28(3), 321–331. https://doi.org/10.22630/PNIKS.2019.28.3.30

Ariault, J.L. (1983). Effective macroscopic description for heat conduction in periodic composites. International Journal of Heat and Mass Transfer, 26(6), 861-869. doi: 10.1016/S0017-9310(83)80110-0

Bensoussan, A., Lions, J.L. & Papanicolaou, G. (2011). Asymptotic Analysis for Periodic Structures. Providence: American Mathematical Society.

Jędrysiak, J. (2010). Termomechanika laminatów, płyt i powłok z funkcyjną gradacją własności [Termomechanics of laminates, plates and shells with functionally graded properties]. Łódź: Wydawnictwo Politechniki Łódzkiej.

Kula, D. (2015). On the existence of the sinusoidal-type temperature fluctuations independently suppressed by the periodic two-phased conducting layer. Acta Scientarum Polonorum Architectura, 63(1), 77-92.

Kula, D. (2016). Ocena wpływu geometrycznej budowy kompozytów periodycznych na intensywność tłumienia fluktuacji obciążeń brzegowych (doctoral dissertation). Łódź: Politechnika Łódzka.

Kula, D. & Wierzbicki, E. (2015). On the Fourier series implementation issue tolerance modeling thermal conductivity of periodic composites. Engineering Transaction, 63(1), 77-92.

Kula, D., Wierzbicki, E., Witkowska-Dobrev, J. & Wodzyński, Ł. (2018). Fourier variant homogenization treatment of one impulse boundary effect behaviour. Mechanics and Mechanical Engineering, 22(3), 683-690.

Michalak, B. (2010). Termomechanika ciał z pewną niejednorodną mikrostrukturą: technika tolerancyjnej aproksymacji [Termomechanics of solids with a certain nonhonmogeneous microstructure: tolerance approximation technique]. Łódź: Wydawnictwo Politechniki Łódzkiej.

Szlachetka, O. & Wągrowska, M. (2011). Boundary effect in a laminated partition with a longitudinal gradation of material properties. Acta Scientarum Polonorum Architectura, 10(3), 27-34.

Wierzbicki, E. (2019). Averaging techniques in thermomechanics of Composite Solids. Surface Localization versus Tolerance Averaging. Warsaw: Warsaw University of Life Sciences Press.

Wierzbicki, E., Kula, D. & Wodzyński, Ł. (2018a). Effective macroscopic description for heat conduction in periodic composites. AIP Conference Proceedings 1922, 140004, 1-8. https://doi.org/10.1063/1.5019146

Wierzbicki, E., Kula, D. & Wodzyński, Ł. (2018b). Fourier variant homogenization of the heat transfer processes in periodic composites. Mechanics and Mechanical Engineering, 22(3), 719-726.

Witkowska-Dobrev, J. & Wągrowska, M. (2015). Zasięg efektu warstwy brzegowej w kompozytach warstwowych dla zagadnień elastostatyki [The area of effect of boundary layer for multilayer composites for stationary elastic problems]. Acta Scientarum Polonorum Architectura, 14(2), 3-17

Wodzyński, Ł., Kula, D. & Wierzbicki, E. (2018). Transport of even and odd temperature fluctuations across the chess-board type periodic composite. Mechanics and Mechanical Engineering, 22(3), 775-787.

Woźniak, C. (ed.). (2009). Thermomechanics of microheterogeneous solids and structures. Tolerance averaging approach. Łódź: Technical University of Łódź Press.

Woźniak, C. (ed.). (2010). Developments in mathematical modeling and analysis of microstructured media. Gliwice: Silesian University Press.

Woźniak, C., Łacińska, L. & Wierzbicki, E. (2005). Boundary and initial fluctuation effect on dynamic behaviour of a laminated solid. Archive of Applied Mechanics, 74, 618-628.

Woźniak, C. & Wierzbicki, E. (2000). Averaging techniques in thermomechanics of composite solids: Tolerance Averaging versus Homogenization. Częstochowa: Technical University of Częstochowa Press.

Woźniak, M., Wierzbicki, E. & Woźniak, C. (2002). A macroscopic model of the diffusion and heat transfer processes in a periodically micro-stratified solid layer. Acta Mechanica 157(1-4), 175-185.



Download data is not yet available.
Recommend Articles